ε$\varepsilon$‐Regularity criteria and the number of singular points for the 3D simplified Ericksen–Leslie system

Abstract

In this paper, we consider the partial regularity of suitable weak solution to the 3D simplify Ericksen–Leslie system modeling the hydrodynamical motion of nematic liquid crystal flow, which is a coupled system with the Navier–Stokes equations for the velocity field and kinematic transport equations for the molecular orientation field. We present a new regularity criteria for suitable weak solutions to the 3D simplified Ericksen–Leslie system. Moreover, under the condition where K is an absolute positive constant. Then for a given open subset and for a given moment of time , the number of points of the set is finite, where and is the set of singular points for .